The search and the analysis of English scientific literature from 2005 to 2020 devoted to the methods of obtaining branched polymers and copolymers of N-isopropylacrylamide were made in order to obtain novel materials with valuable properties. It was found that modern methods of controlled radical polymerization were mainly used for this purpose, namely, atom transfer radical polymerization (ATRP), polymerization with reversible addition-fragmentation chain transfer (RAFT) and group transfer polymerization (GTP).